Convergence and stability analyses of multi-time step algorithm for parabolic systems

Abstract An analysis of the consistency and convergence of a subcycling algorithm together with the stability conditions for parabolic systems of both element and nodal partitions are provided. It is shown that the algorithms only attain a first-order rate-of-convergence for both element and nodal partitions in the sense of the total cycle update. The stability conditions for general integration parameters in an element partition are also given for the first time.